The Daily Telegraph understands that advisers to David Cameron are to study ways of making it cheaper and easier for households to invest in British companies, especially newly-founded firms.

Ministers are also considering using the potential privatisations of state-owned firms like RBS and Royal Mail to give voters shares.

Some Conservatives believe that boosting share-ownership should sit alongside helping more people buy their own homes in party promises to create an “aspiration nation”.

Increasing the number of households with shares in public companies was a major ambition of the Thatcher government, built around the privatisation of major utilities like British Telecom and British Gas.

Despite Lady Thatcher’s ambitions, however, the concentration of shares in the hands of big financial institutions continued. Most households today do not directly own shares, although many have an interest in stock markets through pensions and other investments.

An Office for National Statistics study in 2010 found that barely 10 per cent of the value of shares traded on London exchanges were held by individuals. In 1964 more than half of the UK stock market was held by individuals.

Policies to encouraging share ownership are expected to be considered by a reconfigured Downing Street Policy Unit.

After repeated complaints from MPs and ministers, Mr Cameron is re-staffing the Policy Unit with more Conservative Party aides, who will work on ideas that could inform the party’s general election manifesto.

Until recently, the unit was staffed entirely by civil servants, meaning it worked for both the Coalition parties and could not carry out party-political work for either the Conservatives or Liberal Democrats.

With little more than two years to the next general election, senior Conservatives are increasingly thinking about how to secure the Commons majority that eluded them in 2010

A key priority for the Tories is winning back working-class voters in the north and the Midlands, where marginal seats will decide the outcome of the election.

Some Conservatives believe that Lady Thatcher’s success in winning three general elections in 1979, 1983 and 1987 provides examples of how to win around those voters.

Mr Cameron himself heaped praise on Lady Thatcher yesterday as he launched the Conservative Party’s campaign for next month’s local government elections.

He said: "Margaret Thatcher knew what was right. She stuck to her guns. She saved our country. And I know everyone here is proud that she was not just a great woman and a great Prime Minister but a great Conservative too."

The Conservatives expect to suffer significant losses in the May elections, where they are defending 29 councils.

Those losses could reignite Conservative concerns about Mr Cameron’s strategy, but several MPs said that that the death of Lady Thatcher and recent Labour setbacks have cheered and united the party, reducing the threat to the Prime Minister.